Along with Wallis Simpson, the painter inhabited a brittle elite world that flirted with Hitler as if the fate of millions didn't matter

It seems sadly inevitable. Salvador Dalí was nicknamed ávida dollars ("eager for dollars") by his former friends the surrealists for abandoning idealism in favour of fame and money, and suspected of far worse. He was condemned by the group for his paintingThe Enigma of Hitler. He later wrote that Hitler "turned me on".

Now it turns out he was friends with Wallis Simpson, who has also been suspected of Nazi sympathies. An auction house is about to sell a drawing Dalí gave to the woman for whom Edward VIII abdicated the throne. He did it at his favourite American residence, the St Regis Hotel (it's on their notepaper). Dalí scribbled an affectionate note and sketched a horseman.

It's said that Dalí did the drawing over lunch with the Duchess of Windsor – if so, what did they talk about? Happy memories of the 1930s perhaps. In 1937, just before her marriage to the former monarch, Simpson posed for glamorous photographs by Cecil Beaton in the gardens of a French chateau. This was just a few months after Edward VIII gave up the throne. Beaton portrayed Simpson as a beauty fit to obsess a king – and a subversive modern woman who contrasted with stuffy old Britain and its moralising monarchical ways.

Wallis Simpson and Dalí were both habitues of a brittle elite world that could flirt with Hitler as if the fate of millions of people were a sick joke. After the war, Dalí was happy and rich in Franco's Spain. In New York, he did this sketch for the Duchess of Windsor.

I used to try to see the best in Dalí, but increasingly he looks like one of the 20th century's nastiest cultural products.